Making sounds with analogue electronics - Part 2: Subtractive synthesis

[Part 1 briefly reviews the differences between analogue and digital synthesis, and discusses "one of the major innovations in the development of the synthesizer" - voltage control.]

3.3 Subtractive synthesis
Subtractive synthesis is often mistakenly regarded as the only method of analogue sound synthesis. Although there are other methods of synthesis, the majority of commercial analogue synthesizers use subtractive synthesis. Because it is often presented with a user interface consisting of a large number of knobs and switches, it can be intimidating to the beginner.

Because there is often a one-to-one relationship between the available controls and the knobs and switches, it is well suited to educational purposes. It can also be used to illustrate a number of important principles and models that are used in acoustics and sound theory.

3.3.1 Theory: source and modifier
Subtractive synthesis is based around the idea that real instruments can be broken down into three major parts: a source of sound, a modifier (which processes the output of the source) and some controllers (which act as the interface between the performer and the instrument). This is most obviously apparent in many wind instruments, where the individual parts can be examined in isolation (Figure 3.3.1).

For example, a clarinet, where a vibrating reed is coupled to a tube, can be taken apart and the two parts can be investigated independently. On its own, the reed produces a harsh, strident tone, whilst the body of the instrument is merely a tube that can be shown to have a series of acoustic resonances related to its length, the diameter of the longitudinal hole and other physical characteristic; in other words, it behaves like a series of resonant filters. Put together, the reed produces a sound which is then modified by the resonances of the body of the instrument to produce the final characteristic sound of the clarinet.

Although this model is a powerful metaphor for helping to understand how some musical instruments work, it is by no means a complete or unique answer. Attempting to apply the same concept to an instrument such as a guitar is more difficult, since the source of the sound appears to be the plucked string, and the body of the guitar must therefore be the modifier of the sound produced by the string.

Unfortunately, in a guitar, the source and the modifier are much more closely coupled, and it is much harder to split them into separate parts. For example, the string cannot be played in isolation in quite the same way as the reed of a clarinet can, and all of the resonances of the guitar body cannot be determined without the strings being present and under tension.

FIGURE 3.3.1 The performer uses the instrument controllers to alter the source and modifier parameters.

Despite this, the idea of modifying the output of a sound source is easy to grasp and it can be used to produce a wide range of synthetic and imitative timbres. In fact, the underlying idea of source and modifier is a common theme in most types of sound synthesis.

3.3.2 Subtractive synthesis
Subtractive synthesis uses a subset of this generalized idea of source and modifier, where the source produces a sound that contains all the required harmonic content for the final sound, whilst the modifier is used to filter out any unwanted harmonics and shape the sound's volume envelope. The filter thus 'subtracts' the harmonics that are not required; hence the name of the synthesis method (Figure 3.3.2).

3.3.3 Sources
The sound sources used in analogue subtractive synthesizers tend to be based on mathematics. There are two basic types: waveforms and random. The waveforms are typically named after simple waveshapes: sawtooth, square, pulse, sine and triangle are the most common. The shapes are the ones which are easy to describe mathematically and also to produce electronically. Random waveshapes produce noise, which contains a constantly changing mixture of all frequencies.

Oscillators are related to one of the component parts of analogue synthesizers: function generators. A function generator produces an output waveform, and this can be of arbitrary shape and can be continuous or triggered. An oscillator that is intended to be used in a basic analogue subtractive synthesizer normally produces just a few continuous waveshapes, and the frequency needs to be controlled by a voltage.

The waveshapes in analogue synthesizers are only approximations to the mathematical shapes and the differences give part of the appeal of analogue sounds.

It should also be noted that, in general, sources produce continuous outputs. You need to use a modifier in order to alter the timbre or apply an envelope to the sound.

VCOs
The VCOs provide voltage control of the frequency or pitch of their output. Some VCOs also provide voltage control inputs for modulation (usually FM) and for varying the shape of the output waveforms (usually the pulse width of the rectangular waveshape, although some VCOs allow the shape of other waveforms to be altered as well).

Many VCOs have an additional input for another VCO audio signal, to which the VCO can be synchronized. Hard synchronization forces the VCO to reset its output to keep in sync with the incoming signal, which means that the VCO can only operate at the same or multiple frequencies of the input frequency. This produces a characteristic harsh sound. Other 'softer' synchronization schemes can be used to produce timbral changes in the output rather than locking of the VCO frequency.

A typical VCO has controls for the coarse (semitones) and fine (cents) tuning of its pitch, some sort of waveform selector (usually one of sine, triangle, square, sawtooth and pulse), a pulse width control for the shape of the pulse waveform and an output level control (Figure 3.3.3). Sometimes multiple simultaneous output waveforms are available, and some VCOs also provide 'sub-octave' outputs that are one or two octaves lower in pitch. A CV for the pulse width allows the shape of the pulse waveform (and sometimes other waveforms as well) to be altered. This is called pulse width modulation (PWM) or shape modulation.